The Affective Behavior Analysis in-the-wild (ABAW) 2020 Competition is the first Competition aiming at automatic analysis of the three main behavior tasks of valence-arousal estimation, basic expression recognition and action unit detection. It is split into three Challenges, each one addressing a respective behavior task. For the Challenges, we provide a common benchmark database, Aff-Wild2, which is a large scale in-the-wild database and the first one annotated for all these three tasks. In this paper, we describe this Competition, to be held in conjunction with the IEEE Conference on Face and Gesture Recognition, May 2020, in Buenos Aires, Argentina. We present the three Challenges, with the utilized Competition corpora. We outline the evaluation metrics, present both the baseline system and the top-3 performing teams' methodologies per Challenge and finally present their obtained results. More information regarding the Competition, the leaderboard of each Challenge and details for accessing the utilized database, are provided in the Competition site: http://ibug.doc.ic.ac.uk/resources/fg-2020-competition-affective-behavior-analysis.